This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372415 #11 Apr 30 2024 06:08:59
%S A372415 1,2,10,59,366,2332,15121,99276,657894,4391438,29482320,198865680,
%T A372415 1346655921,9149295482,62336961732,425760311734,2914151872614,
%U A372415 19983724103726,137267022656710,944287970305935,6504676822047876,44861522295224400,309742638630690264
%N A372415 Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x)^3 )^n.
%F A372415 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(3*n-2*k-1,n-3*k).
%F A372415 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^3) ). See A366052.
%o A372415 (PARI) a(n, s=3, t=1, u=3) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
%Y A372415 Cf. A372413, A372414.
%Y A372415 Cf. A366052.
%K A372415 nonn
%O A372415 0,2
%A A372415 _Seiichi Manyama_, Apr 29 2024